Question

University of Minnesota recently developed a new apple called First Kiss. At the Minnesota State Fair, 200 random fair goers sampled both the new apple and a Honeycrisp apple and asked which apple they preferred. Of the 200 people, 134 people preferred First Kiss and the remaining 66 people preferred Honeycrisp. Is there any preference between the two apples? Use α =0.05 to perform a 5-step test of hypothesis.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.50
Alternative hypothesis: P 0.50

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.03536
z = (p - P) /S.D

z = 4.81

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -4.81 or greater than 4.81.

Thus, the P-value = less than 0.001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that there is preferenace between the two apples.